Mechanics 5 Edexcel Rotational stuff Watch
Surely the particle add mass onto the lamina but its vertical velocity does not increase the angular speed of the lamina?
I can't see any reason for giving the height (l) of the particle above the lamina. Its kinetic energy from falling is simply going to be absorbed by the lamina, but won't affect the rotational energy of it (the lamina).
What will affect the lamna will be the sudden addition of a mass at one of its corners. This is going to increase the inertia of the new lamina and hence reduce its angular velocity.
I would find the inertia of the lamina before and after the 3m mass attached itself and use conservation of angular momentum to work out the new angular velocity in terms of the old angular velocity.
Edit: no it doesn't, as pointed out below. I misunderstood the axis of rotation; it would help if I read the question properly. The line below is also wrong for the same reason.
(If you think about the case where the lamina isn't rotating, it's obvious that an off-centre impact is going to cause rotation).
If you think about the case where the lamina isn't rotating, it's obvious that an off-centre impact is going to cause rotation.
Teach me to read the question properly...
Not reading the question is a sign of genius. ...